Question: The sum of $6$ consecutive integers is $393$. What is the third number in this sequence?
Solution: Call the first number in the sequence $x$. The next integer in the sequence is $x + 1$ The sum of the $6$ consecutive integers is: $x+ (x + 1)+ (x + 2)+ (x + 3)+ (x + 4)+ (x + 5) = 393$ $6x + 15= 393$ $6x = 378$ $x = 63$ Since $x$ is the first number, $x + 2$ is the third integer. Thus, the third number in the sequence is $65$.